Sometimes, I look at a triangle and imagine me inside, going around from side to side, trying to figure out where to go next and what should I do. Of course once trapped inside a triangle, there is no escape because you are surrounded by walls, which can even expand upwards in the z-direction.
Stepping inside a triangle is always tricky, because you have three locked lines, so the only way to come in is from the top down, or below up. The surface of the triangle can be smooth and can be rigid, but in general it is smooth, which makes walking on it much easier of course. It would be nice to claim a triangle, just inserting a big flag in the middle and say " from now on, this belongs to purgatory72." Nice feeling :). Probably surround the flag with a couple of huge rocks to make sure no one takes it out, plus it brings balance inside the triangle in case of sudden shifts in the upper universe and rotation of the axis around.
Well thats my geometrical thought of the day, hope you liked it